Counting Defiers

17 Pages Posted: 19 Mar 2019

See all articles by Amanda Kowalski

Amanda Kowalski

University of Michigan at Ann Arbor - Department of Economics

Date Written: March 2019


The LATE monotonicity assumption of Imbens and Angrist (1994) precludes “defiers,” individuals whose treatment always runs counter to the instrument, in the terminology of Balke and Pearl (1993) and Angrist et al. (1996). I allow for defiers in a model with a binary instrument and a binary treatment. The model is explicit about the randomization process that gives rise to the instrument. I use the model to develop estimators of the counts of defiers, always takers, compliers, and never takers. I propose separate versions of the estimators for contexts in which the parameter of the randomization process is unspecified, which I intend for use with natural experiments with virtual random assignment. I present an empirical application that revisits Angrist and Evans (1998), which examines the impact of virtual random assignment of the sex of the first two children on subsequent fertility. I find that subsequent fertility is much more responsive to the sex mix of the first two children when defiers are allowed. [This paper has been combined with “A Model of a Randomized Experiment with an Application to the PROWESS Clinical Trial” ( and superseded by “Counting Defiers: Examples from Health Care” ( as of July 17, 2020.]

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Suggested Citation

Kowalski, Amanda, Counting Defiers (March 2019). NBER Working Paper No. w25671, Available at SSRN:

Amanda Kowalski (Contact Author)

University of Michigan at Ann Arbor - Department of Economics ( email )

Ann Arbor, MI
United States

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